# Mathematics

**Mathematics Intent at PTM**

The intent of our mathematics curriculum is to design a curriculum, which is accessible to all and will maximise the development of every child’s ability and academic achievement. We endeavour to deliver lessons that are challenging and engaging. We want children to make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly difficult problems. We intend for our pupils to be able to apply their mathematical knowledge to science and across other areas of their Experience units. As our pupil’s progress, we intend for our pupils to be able to understand the world, to reason mathematically, to tackle challenging problems and to have a sense of enjoyment and curiosity about the subject.

Teaching and Learning – Maths is taught using Primary Stars in KS1, the White Rose mastery scheme in KS2. In EYFS (Early Years Foundation Stage), Numicon is used to embed number facts. In Pre-school pupils learn the numbers from 0-3, in Nursery: the numbers to 5, and in Reception, they learn the number bonds to 10 and can count up to 20. There is a greater focus on number in EYFS, especially in their learning environments but learning about shape is also evident.

Arithmetic skills are taught regularly morning work in Years 3 to 6 to help develop fluency and these skills are tested weekly. Each ‘step’ of learning’ will include an element of reasoning or a problem-solving activity chosen from White Rose, using past SATS questions or from ‘I See Problem Solving’. The expectation is that each lesson begins with a flashback or a revision starter- 15mins to build on either fluency or retention skills. Pupils should also be taught multiplication skills (Yr. 2- Yr. 6) and should be allocated time in the classroom to practise them, in preparation for their weekly test. In Years 5 and 6, pupils learn to recall squared and cubed number facts and the times tables from 13x upwards, having completed the MTC in Year 4, so as not to impede further mathematical development. In order to build on retention skills, teachers have been provided with a bank of questions for their year group, to ask during registration or whilst lining up etc.

**Why White Rose?**

At P.T.M, we decided to use the White Rose scheme because it is a mastery approach that had been successfully embedded in other schools and came recommended for teaching of fluency and reasoning skills. It is also much more cost effective and was relatively easy to implement in our school, in September 2021. In KS1, the Primary Stars scheme is used, as it aligns with the White Rose scheme of work, yet the resources are more engaging for pupils to use. Primary Stars also provides interesting problem-solving activities, whilst White Rose does not. Previously, we had been using the Power Maths Scheme, which was not only expensive to use, but it also provided less scope for teachers to be creative in their teaching of maths. Since September 2021, our teaching staff have grown increasingly confident in their usage of the WR scheme, which follows a clear progression

model and addresses the previous year’s objectives, which helped to bridge any gaps in learning, as part of our COVID-19 catch-up recovery plan. Our current step is to build on the teaching and learning of conceptual and procedural maths so that pupils can become more proficient in tackling reasoning and problem-solving activities. Pupils have been equipped with STEM sentences, resources and problem solving strategies to help support this development.

**Primary Stars and White Rose Outline Structure**

The White Rose scheme of work ensures that the yearly objectives are covered, and that each year group is being taught the skills necessary to become a successful practitioner. It also provides a variety of resources for reasoning and problem-solving, as well as a ‘flashback’ resource, which is used to assess previous learning. At the end of every unit, there is an assessment tool, which helps to monitor gaps in learning. Teachers are assessing retrieval by giving pupils the assessment to take, two to three weeks after it has been taught. They can then, assess what further teaching needs to be carried out, to tackle any areas of weakness or misconceptions.

**Cross-curricular Links**

Although Maths is allocated specific lesson times, teachers have been asked to explicitly apply the learned skills in activities planned, where applicable, in other subjects such as Science (measure and data handling), DT- (measure), Art (shape, patterns and symmetry), Forest School and Computing (data handling), and in any Experience lesson in which there are practical application opportunities. Here are some examples or where it is being used across the curriculum:

**DT- Year 1**

Session 10 -DT How do you design a toy?

LO- I can design a toy from the past. Link to maths- shape what shapes would you need to draw. What shapes are different objects that you will use.

**History- Year 2**

Session 3- History. To develop an awareness of the past in the context of comparing present-day London to the London that existed before 1666.

L.O – I can find out some of the ways in which London has changed.

Start off by talking about events that have happened in the past of the children’s lives and put them into a timeline e.g., year of birth, started school, etc. or timeline of the week to discuss events.

Use the Timeline Year Cards to distribute amongst children in pairs/groups. Can the children organise themselves in order from earliest year to the most recent? Children to place the years into order and explain that the year 1666 was around 350 years ago and that this was an important time in British history that you will be focusing on.

**Computing-Year 3**

Lesson 1- Connecting Computers

Maths (lesson 1)

Number and place value: Solve number problems and practical problems

**Lesson 1:** You will need an understanding of digital and non-digital devices. The key difference is that a digital device is capable of some processing, i.e., it has functions beyond being either on or off. You will also need to be familiar with the concept of input, process, output (IPO) which underpins all digital devices. There are cross-curricular links with maths for IPO which can be referenced during this lesson.

**Art- Sculpture Year 4**

Session 7 and 8 – L.O – I can use discarded items to create a sculpture (Art, DT, Maths)

**Cross-curricular link to Maths – Measurement in the planning process.**

**Art- Year 5**

Session 13:

LO: To explore the work of Michelangelo

LO: To gain an understanding of proportion

Explain how great artists, like Botticelli and Michelangelo, would use the correct proportions of people and animals in order to make them look realistic. Explain some of the proportions that humans have (foot length = lower arm length, height = arm span, etc.)

**Geography- Year 6:**

Session 4/5/6 – Fieldwork element of Geography

LO: To create an observational survey of the local area to collect data (Survey-link to ambition, future etc)

Children to go to Bush Fair to observe and tally all of the different job opportunities they can see there.

During Maths Week (November 2021), teachers also taught lessons that were themed using the Experience that was being taught at the time.

**Progression**

The mastery approach is used across the school. Primary Stars, which is more child-friendly and as aforementioned, aligns with the White Rose Scheme, is used in KS1 and White Rose is used in KS2. The fact that both resources use the same progression model (WR) allows for clear progression of the subject year-on- year. The Early Years Curriculum is followed in all EYFS settings. Through observations, moderation and book looks, the progression of mathematical concepts is evident in books, key vocabulary is being used with STEM sentences to explain learning and pupil’s presentation and number formation skills are being monitored.

**Delivery of Maths**

Teachers are guided to use a range of concrete, pictorial and abstract resources in lessons. Many lessons are well-resourced, and teachers often use a variety of concrete resources to help support different learners, depending on the unit being taught. As pupils progress throughout the school, there is often less dependency on using some of the concrete resources, yet their usage is encouraged to embed key skills. In the teaching of place value, number bonds and column method, for example, Dienes, multi-link and counters are used in KS1 and in KS2, whereas Numicon is used in EYFS and Yr 1.

Pupils are encouraged to explain their reasoning and reflect on their learning, as well as to develop the skills of resilience, problem-solving and teamwork in lessons. In many lessons observed, pupils were given tasks, ranging from mini ‘Think, Pair, Share’ activities to complete, to working out the most effective methods used through partner, group and whole-class discussion. Such activities, demand that pupils reflect on their learning and communicate their understanding, using mathematical language, as an individual, partnership or team.

Pupils are given regular feedback through live or feedback in their books. Assessment, in the forms of White Rose- end of unit assessments, previous SATS papers (in Yrs 2 and 6) and NFER

assessments, are used to monitor gaps in pupil’s learning. In Year 6, pupils are put in ability booster groups to help bridge gaps and prepare for their KS2 SATS assessments.

**How learning barriers are overcome:**

Quality First Teaching is evident in classrooms where all abilities are being challenged and supported with their specific needs. Using data from assessments to address any gaps in learning, interventions are also taking place, and especially in KS2, to help those who need any extra help. Children who are SEND or EAL can access the maths teaching due to the use of visuals, concrete resources and diagrams to support understanding. Where needed, lessons are also adapted in class by adult support or by peer pairing.

**What is taught in each key stage:**

**Year 1 programme of study**

**Number – number and place value**

**Pupils should be taught to:**

· count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

· count, read and write numbers to 100 in numerals; count in multiples of 2s, 5s and 10s

· given a number, identify 1 more and 1 less

· identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

· read and write numbers from 1 to 20 in numerals and words

**Number – addition and subtraction**

**Pupils should be taught to:**

· read, write and interpret mathematical statements involving addition (+), subtraction (−) and equals (=) signs

· represent and use number bonds and related subtraction facts within 20

· add and subtract one-digit and two-digit numbers to 20, including 0

· Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 =? – 9

**Number – multiplication and division**

**Pupils should be taught to:**

· Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

**Number – fractions**

**Pupils should be taught to:**

· recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity

· Recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity.

**Measurement**

**Pupils should be taught to:**

· compare, describe and solve practical problems for:

. lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]

. mass/weight [for example, heavy/light, heavier than, lighter than]

. capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]

. time [for example, quicker, slower, earlier, later]

**measure and begin to record the following:**

- lengths and heights
- mass/weight
- capacity and volume
- time (hours, minutes, seconds)
- recognise and know the value of different denominations of coins and notes
- sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]

· Recognise and use language relating to dates, including days of the week, weeks, months and years

· tell the time to the hour and half past the hour and draw the hands on a clock face to show these times

**Geometry – properties of shapes**

**Pupils should be taught to:**

**recognise and name common 2-D and 3-D shapes, including:****2-D shapes [for example, rectangles (including squares), circles and triangles]****3-D shapes [for example, cuboids (including cubes), pyramids and spheres]**

**Geometry – position and direction**

Pupils should be taught to:

· describe position, direction and movement, including whole, half, quarter and three-quarter turn

**Year 2 programme of Study**

**Number – number and place value**

**Pupils should be taught to:**

· count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward

· recognise the place value of each digit in a two-digit number (10s, 1s)

· identify, represent and estimate numbers using different representations, including the number line

· compare and order numbers from 0 up to 100; use <, > and = signs

· read and write numbers to at least 100 in numerals and in words

· use place value and number facts to solve problems

**Number – addition and subtraction**

**Pupils should be taught to:**

- solve problems with addition and subtraction:
- using concrete objects and pictorial representations, including those involving numbers, quantities and measures
- applying their increasing knowledge of mental and written methods

- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
- a two-digit number and 1s
- a two-digit number and 10s
- 2 two-digit numbers
- adding 3 one-digit numbers

- show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot
- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

**Number – multiplication and division**

**Pupils should be taught to:**

- recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
- calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
- show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot
- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

**Number – fractions**

**Pupils should be taught to:**

· recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity

· write simple fractions, for example of 6 = 3 and recognise the equivalence of and

**Measurement**

**Pupils should be taught to:**

· choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

· compare and order lengths, mass, volume/capacity and record the results using >, < and =

· recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

· find different combinations of coins that equal the same amounts of money

· solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

· compare and sequence intervals of time

· tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times

· know the number of minutes in an hour and the number of hours in a day

**Geometry – properties of shapes**

**Pupils should be taught to:**

· identify and describe the properties of 2-D shapes, including the number of sides, and line symmetry in a vertical line

· identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

· identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

· compare and sort common 2-D and 3-D shapes and everyday objects

**Geometry – position and direction**

**Pupils should be taught to:**

· order and arrange combinations of mathematical objects in patterns and sequences

· use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

**Statistics**

**Pupils should be taught to:**

· interpret and construct simple pictograms, tally charts, block diagrams and tables

· ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity

· ask-and-answer questions about totalling and comparing categorical data

**KS2**

**Year 3 programme of study**

**Number – number and place value**

**Pupils should be taught to:**

· count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

· recognise the place value of each digit in a 3-digit number (100s, 10s, 1s)

· compare and order numbers up to 1,000

· identify, represent and estimate numbers using different representations

· read and write numbers up to 1,000 in numerals and in words

· solve number problems and practical problems involving these ideas

**Number – addition and subtraction**

**Pupils should be taught to:**

- add and subtract numbers mentally, including:
- a three-digit number and 1s
- a three-digit number and 10s
- a three-digit number and 100s

- add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
- estimate the answer to a calculation and use inverse operations to check answers
- solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

**Number – multiplication and division**

**Pupils should be taught to:**

· recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

· write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

· solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

**Number – fractions**

**Pupils should be taught to:**

· count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

· recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

· recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

· recognise and show, using diagrams, equivalent fractions with small denominators

· add and subtract fractions with the same denominator within one whole [for example, + = ]

· compare and order unit fractions, and fractions with the same denominators

· solve problems that involve all of the above

**Measurement**

**Pupils should be taught to:**

· measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

· measure the perimeter of simple 2-D shapes

· add and subtract amounts of money to give change, using both £ and p in practical contexts

· tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks

· estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnight

· know the number of seconds in a minute and the number of days in each month, year and leap year

· compare durations of events [for example, to calculate the time taken by particular events or tasks]

**Geometry – properties of shapes**

**Pupils should be taught to:**

· draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

· recognise angles as a property of shape or a description of a turn

· identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle

· identify horizontal and vertical lines and pairs of perpendicular and parallel lines

**Statistics**

**Pupils should be taught to:**

· interpret and present data using bar charts, pictograms and tables

· solve one-step and two-step questions [for example ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables

**Year 4 programme of study**

Number – number and place value

Pupils should be taught to:

· count in multiples of 6, 7, 9, 25 and 1,000

· find 1,000 more or less than a given number

· count backwards through 0 to include negative numbers

· recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)

· order and compare numbers beyond 1,000

· identify, represent and estimate numbers using different representations

· round any number to the nearest 10, 100 or 1,000

· solve number and practical problems that involve all of the above and with increasingly large positive numbers

· read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value

**Number – addition and subtraction**

**Pupils should be taught to:**

· add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

· estimate and use inverse operations to check answers to a calculation

· solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

**Number – multiplication and division**

**Pupils should be taught to:**

· recall multiplication and division facts for multiplication tables up to 12 × 12

· use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers

· recognise and use factor pairs and commutatively in mental calculations

· multiply two-digit and three-digit numbers by a one-digit number using formal written layout

· solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

**Number – fractions (including decimals)**

**Pupils should be taught to:**

· recognise and show, using diagrams, families of common equivalent fractions

· count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

· solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

· add and subtract fractions with the same denominator

· recognise and write decimal equivalents of any number of tenths or hundreds

· recognise and write decimal equivalents to , ,

· find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

· round decimals with 1 decimal place to the nearest whole number

· compare numbers with the same number of decimal places up to 2 decimal places

· solve simple measure and money problems involving fractions and decimals to 2 decimal places

**Measurement**

**Pupils should be taught to:**

· convert between different units of measure [for example, kilometre to metre; hour to minute]

· measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

· find the area of rectilinear shapes by counting squares

· estimate, compare and calculate different measures, including money in pounds and pence

· read, write and convert time between analogue and digital 12- and 24-hour clocks

· solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days

**Geometry – properties of shapes**

**Pupils should be taught to:**

· compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

· identify acute and obtuse angles and compare and order angles up to 2 right angles by size

· identify lines of symmetry in 2-D shapes presented in different orientations

· complete a simple symmetric figure with respect to a specific line of symmetry

**Geometry – position and direction**

**Pupils should be taught to:**

· describe positions on a 2-D grid as coordinates in the first quadrant

· describe movements between positions as translations of a given unit to the left/right and up/down

· plot specified points and draw sides to complete a given polygon

**Statistics**

**Pupils should be taught to:**

· interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

· solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

**Year 5 programme of study**

**Number – number and place value**

**Pupils should be taught to:**

· read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit

· count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000

· interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0

· round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000

· solve number problems and practical problems that involve all of the above

· read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

**Number – addition and subtraction**

**Pupils should be taught to:**

· add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

· add and subtract numbers mentally with increasingly large numbers

· use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

· solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

**Number – multiplication and division**

**Pupils should be taught to:**

· identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers

· know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

· establish whether a number up to 100 is prime and recall prime numbers up to 19

· multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

· multiply and divide numbers mentally, drawing upon known facts

· divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

· multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000

· recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

· solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes

· solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

· solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

**Number – fractions (including decimals and percentages)**

**Pupils should be taught to:**

· compare and order fractions whose denominators are all multiples of the same number

· identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

· recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, + = = 1 ]

· add and subtract fractions with the same denominator, and denominators that are multiples of the same number

· multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

· read and write decimal numbers as fractions [for example, 0.71 = ]

· recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

· round decimals with 2 decimal places to the nearest whole number and to 1 decimal place

· read, write, order and compare numbers with up to 3 decimal places

· solve problems involving number up to 3 decimal places

· recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction

· solve problems which require knowing percentage and decimal equivalents of , , , , and those fractions with a denominator of a multiple of 10 or 25

**Measurement**

**Pupils should be taught to:**

· convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]

· understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

· measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

· calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes

· estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]

· solve problems involving converting between units of time

· use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

**Geometry – properties of shapes**

**Pupils should be taught to:**

- identify 3-D shapes, including cubes and other cuboids, from 2-D representations
- know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
- draw given angles, and measure them in degrees (°)
- identify:
- angles at a point and 1 whole turn (total 360°)
- angles at a point on a straight line and half a turn (total 180°)
- other multiples of 90°
- use the properties of rectangles to deduce related facts and find missing lengths and angles
- distinguish between regular and irregular polygons based on reasoning about equal sides and angles

**Geometry – position and direction**

**Pupils should be taught to:**

· identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

**Statistics**

**Pupils should be taught to:**

· solve comparison, sum and difference problems using information presented in a line graph

· complete, read and interpret information in tables, including timetables

**Year 6 programme of study**

**Number – number and place value**

**Pupils should be taught to:**

· read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit

· count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000

· interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0

· round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000

· solve number problems and practical problems that involve all of the above

· read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

**Number – addition, subtraction, multiplication and division**

**Pupils should be taught to:**

· multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

· divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

· divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

· perform mental calculations, including with mixed operations and large numbers

· identify common factors, common multiples and prime numbers

· use their knowledge of the order of operations to carry out calculations involving the 4 operations

· solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

· solve problems involving addition, subtraction, multiplication and division

· use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

**Number – Fractions (including decimals and percentages)**

**Pupils should be taught to:**

· use common factors to simplify fractions; use common multiples to express fractions in the same denomination

· compare and order fractions, including fractions >1

· add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

· multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, × = ]

· divide proper fractions by whole numbers [for example, ÷ 2 = ]

· associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ]

· identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places

· multiply one-digit numbers with up to 2 decimal places by whole numbers

· use written division methods in cases where the answer has up to 2 decimal places

· solve problems which require answers to be rounded to specified degrees of accuracy

· recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

**Ratio and proportion**

**Pupils should be taught to:**

· solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts

· solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison

· solve problems involving similar shapes where the scale factor is known or can be found

· solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

**Algebra**

**Pupils should be taught to:**

· use simple formulae

· generate and describe linear number sequences

· express missing number problems algebraically

· find pairs of numbers that satisfy an equation with 2 unknowns

· enumerate possibilities of combinations of 2 variables

**Measurement**

**Pupils should be taught to:**

· solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate

· use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places

· convert between miles and kilometres

· recognise that shapes with the same areas can have different perimeters and vice versa

· recognise when it is possible to use formulae for area and volume of shapes

· calculate the area of parallelograms and triangles

· calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]

**Geometry – properties of shapes**

**Pupils should be taught to:**

· draw 2-D shapes using given dimensions and angles

· recognise, describe and build simple 3-D shapes, including making nets

· compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

· illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

· recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

**Geometry – position and direction**

**Pupils should be taught to:**

· describe positions on the full coordinate grid (all 4 quadrants)

· draw and translate simple shapes on the coordinate plane, and reflect them in the axes

**Statistics**

**Pupils should be taught to:**

· interpret and construct pie charts and line graphs and use these to solve problems

· calculate and interpret the mean as an average

**Parental Support:**

To further aid your child in their mathematical development, there are many websites which are fun, engaging and easy to access at home. Please see the list below:

**EYFS, KS1 and KS2**

This website provides free worksheets, interactive activities and other resources to help with the learning of mathematics facts and skills in the Foundation Stage, Key Stage 1 and Key Stage 2.

http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml

This free website not only has a selection of interactive maths games but it also has videos that will help clarify some areas of maths that can be difficult to understand. Suitable for Foundation Stage, KS1 and KS2.

http://www.oxfordowl.co.uk/home/maths-owl/maths

Although this website is free, you need to join in order to download ebooks to support with your child’s learning. It has lots of activities, simple ideas and top tips to offer on how to help your child understand key concepts of the curriculum. Suitable for Foundation Stage, KS1 and KS2.

http://www.topmarks.co.uk/Interactive.aspx?cat=1

There are many tablet friendly resources available on this website to help build on your child’s learning at home. Suitable for Foundation Stage, KS1 and KS2.

**KS1 and KS2 only**

http://www.ttrockstars.com http://www.primaryhomeworkhelp.co.uk/maths/

A free and interactive website with lots of games to help consolidate areas of the maths curriculum in a fun and engaging way. Suitable for both KS1 and KS2.

**KS2 only**

http://www.mad4maths.com/parents/

This interactive website caters for parents who need clarification regarding areas of the KS2 maths curriculum. It is very detailed as it shows the objectives that need to be covered in each year group as well as providing tips and strategies to overcome barriers to learning. Suitable for KS2 only

http://www.crickweb.co.uk/ks2numeracy.html

On this website there are many kids’ games and resources that will help support your child with maths at home. The interactive resources include cool maths games. Suitable for KS2